PRL 111, 268101 (2013)
PHYSICAL REVIEW LETTERS
week ending 27 DECEMBER 2013
Nonequilibrium Collective Dynamics in Photoexcited Lipid Multilayers by Time Resolved Diffuse X-Ray Scattering T. Reusch,1,* D. D. Mai,1 M. Osterhoff,1 D. Khakhulin,2 M. Wulff,2 and T. Salditt1,* 1
Institut fu¨r Ro¨ntgenphysik, Georg-August-Universita¨t Go¨ttingen, Friedrich-Hund-Platz 1, 37077 Go¨ttingen, Germany 2 European Synchrotron Radiation Facility (ESRF), 6 rue Jules Horowitz, 38000 Grenoble, France (Received 7 June 2013; published 26 December 2013) We study the nonequilibrium shape fluctuations in fluorescence labeled phospholipid multibilayers composed of the model lipid DOPC and the well-known lipid dye Texas red, driven out of equilibrium by short laser pulses. The temporal evolution of the lipid bilayer undulations after excitation was recorded by time resolved x-ray diffraction. Already at moderate peak intensities (Pp 105 W=cm2 ), pulsed laser illumination leads to significant changes of the undulation modes in a well-defined lateral wavelength band. The observed phenomena evolve on nano- to microsecond time scales after optical excitation, and can be described in terms of a modulation instability in the lipid multilamellar stack. DOI: 10.1103/PhysRevLett.111.268101
PACS numbers: 87.16.dj, 05.70.Ln, 87.64.Bx, 87.64.kv
Excitation of embedded fluorophores in biomolecular assemblies is a ubiquitous tool in modern biophysics. Despite the excitations from the molecular ground state of the fluorophores, it is tacitly assumed in most experiments that the supramolecular collective states of the entire biomolecular assembly remain unchanged, apart perhaps from more or less negligible heat generation. At the same time, it is well understood that collective modes in soft matter systems can easily be excited, and that even small local forces or energy can lead to a rather large structural response. More generally, all active and all living systems are intrinsically out of thermal equilibrium, in many cases driven by a multitude of local force centers and by energy release on molecular scales, for example, due to metabolism. From a fundamental point of view, the understanding of the dissipation pathway from local energy input to heat, eventually accompanied by various collective modes, remains mysterious in many cases. For the important case of membranes, considered to be nature’s most important interface, nonequilibrium fluctuations driven by active force centers, such as proteins, have been addressed in a number of theoretical studies [1–7]. On the contrary, on the experimental side only few studies, for example, by micropipette aspiration and optical microscopy, have tried to address this challenging issue [8–10]. In this work we show that photoexcitation of individual fluorophores in a labeled lipid membrane can lead to a collective response and address the question over which pathway and on which time scales structural dynamics evolve. We have investigated fluorescently labeled phospholipid multibilayers composed of the model lipid
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
0031-9007=13=111(26)=268101(5)
1,2-Dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) and the well-known lipid dye Texas red [11,12] by time resolved x-ray scattering after excitation by a nanosecond laser pulse, covering a broad range of well-matched length and time scales from near-molecular to the mesoscopic range. The evolution of the membrane height-height correlation functions was monitored by recording the diffuse (nonspecular) x-ray reflectivity in a stroboscopic manner synchronized to the periodic optical excitation. In this laser-pump x-ray-probe scheme, pronounced deviations of the collective undulation spectra from thermal equilibrium are observed, which is usually described within linearized smectic elasticity, based on two elastic coefficients, the compressional modulus B and the bending modulus K ¼ =d, where is the single bilayer bending rigidity and d the lamellar periodicity [13]. Figure 1(a) shows a schematic of the ‘‘optical pump–x-ray-probe’’ principle used to characterize the structural and dynamical response of the fluorophore labeled lipid membranes to pulsed laser illumination. (1) Membrane dynamics are excited (or pumped) by a short nanosecond laser pulse. (2) At a well-defined time delay t after the excitation, the instantaneous sample structure is probed by a short ( 50 ps) x-ray pulse. (3) The pump-probe scheme is repeated in a stroboscopic manner for each time delay t until a suitable signal-to-noise ratio is reached. Changing t now allows us to observe characteristic changes in the membrane height-height correlation functions following a short pulse excitation, in particular, by extracting the fundamental length scales describing the collective membrane undulations as a function of t: (i) the lamellar periodicity d, (ii) the rms-fluctuation amplitude ¼ hui ðrÞ2 ir;i (i denotes the index of bilayer in the multilamellar stack), (iii) the in-plane correlation length r , and (iv) the vertical correlation length z ðqr Þ ¼ 1=ðq2r Þ, which describes the correlation length in the direction z normal to the membranes, for an undulation with lateral
268101-1
Published by the American Physical Society
0
10
(b)
t
probe-pulse 0.20 pump-pulse nm 1.)
(g)
-4
10
-5
1st. order
1st. order S(n,qr) ~ qr qr* = 1.7·10 -3Å -1, = -2.4 -3
10
-2
II(1,t)
kf 0.05
10
12
(c)
1.10
1.05
PB
3.) 0
0.04 0.08 qr [1/Å]
-0.01
undulation modes
-1
qr [Å-1]10
x 10 1.20 FWHM qz 1.15
0 qr [1/Å]
0.01
d
(f)
-1
0.10 2.)
-3
lateral correlation length r
transverse correlation length z
-2
10
qz [1/Å]
1.) excitation 2.) measurement 3.) relaxation
(d)
10
10
qz [1/Å]
ki
SB 0.15
HWHM (qr*)
-1
10
FWHMqz [1/Å]
0.25
ki
S(n,qr) [a.u.]
(a)
week ending 27 DECEMBER 2013
PHYSICAL REVIEW LETTERS
PRL 111, 268101 (2013)
x 10
10
-3
FWHM of 1st. reflection
2 qr2 +
res
8 6
(e)
4 2 0
1
2
3 4 qr [1/Å]
5
x 10-3 7 6
FIG. 1 (color). (a) Schematic of a laser pump–x-ray-probe measurement on a multilamellar lipid stack in the fluid L phase. The temporal evolution of membrane undulations is studied in response to a short pulse excitation, by recording the diffuse scattering pattern and line shape analysis of the individual lamellar reflections. (b) Example of a lamellar diffraction pattern with primary beam (PB), specular beam (SB), and the two first lamellar diffraction orders, with (c) a close-up of the first order reflection n ¼ 1. From the two-dimensional distribution, the lateral decay with qr as shown in (d) and the width in direction of qz as shown in (e) are extracted, to yield the temporal evolution of (f) lateral r and vertical z correlation lengths, respectively. (g) Sample chamber for oriented Texas red labeled lipid multilayers fully immersed in solution.
wave number qr . In thermal equilibrium the prefactor is pffiffiffiffiffiffiffiffiffiffi given by the so-called smectic penetration length K=B. These length scales and correlation functions are derived from the measured structure factor Sðqz ; qr Þ, which describes the diffuse intensity distribution around the equidistant lamellar diffraction orders at qz ¼ nð2=dÞ. To this end the Sðqr ; qz Þ measured for each time delay is analyzed as follows. First, intensity is integrated in the range qz ðnÞ ð=dÞ for each diffraction order n, resulting in a structure factor Sðn; qr Þ of an average single bilayer [14]. Sðn; qr Þ exhibits a rather flat plateau for qr qr ¼ 2=r and then falls off with a characteristic power law decay Sðn;qr Þ / aq r at large qr [14]; see Fig. 1(d). For qz 1, in particular, for n ¼ 1, the width qr of the plateau is a measure of the in-plane correlation length r ¼ ð2=HWHMÞ and Sðqr ; qz Þ is identified with the Fourier transform of the in-plane self-correlation function of an average bilayer. In a second step, is extracted from the increase of the Bragg sheet width along qz as a function of qr , see Fig. 1(e), characterizing the height-height crosscorrelation between different bilayers, as detailed in the Supplemental Material [15]. The experimental data shown here were recorded on highly oriented DOPC multilayers (N 1300 bilayers) containing 5 mole % Texas red labeled DHPE (headgroup labeled). Samples were fully immersed in a solution containing 30 wt % polyethylene glycol (corresponding to an osmotic stress of 1.54 MPa), preventing destabilization of the multilayers [16,17]. The 17 keV x-ray undulator beam impinged onto the sample at angle of incidence i 0:5 . Stroboscopic data accumulation was carried out at a repetition rate of f 1 kHz [18] with synchronized optical pumping using ¼ 527 nm, well matched to the edge of the absorption spectrum of Texas red [11]. The standard
laser pulse duration was 180 ns, while some data were recorded at increased temporal resolution of 5 ns, roughly corresponding to the lifetime of the excited state. Full details are given in the Supplemental Material [15,19]. Figure 2 shows the temporal evolution of the diffuse scattering intensity pattern highlighting the main changes in the line shape, followed by Fig. 3 which presents the relative changes in all observables extracted from the first diffraction order. The first generic observable is the time dependent integrated intensity IIðn; tÞ of the individual reflection orders n, as plotted in Fig. 2(a) for n ¼ 1 and four different pump energies Ep . A sharp intensity increase within the first 1 s after optical excitation is observed in all cases, the functional form of IIðn; tÞ as well as the relative amplitude both depend on the pump energy Ep as well as n. The rise time of the initial intensity increase shortens with pump energy, from t 1 s for Ep 100 J to t 100 ns for Ep 1000 J. Relaxation to thermal equilibrium takes place on the 10 s time scale, and the system has fully relaxed after t ¼ 100 s in all cases. A distinct second intensity maximum at t 40 s is observed for the second diffuse order; see Fig. S1 in the Supplemental Material [15]. The fast intensity increase can be linked to an increased positional disorder of the membranes upon laser excitation. The intensity relaxation on the s time scale (a broad plateau for Ep 500 J) can be attributed to the energy dissipation via collective modes, possibly a collective undulation amplitude. The bilayer as determined periodicity dðtÞ ¼ ðn2=qz ðnÞÞ ¼ 53:6 A from peak positions (center of mass) remains unchanged in all cases. Next, line shape changes were investigated in addition to the intensity; see Figs. 2(b) and 2(c). The lateral momentum dependence of the integrated structure factor Sðn; qr ; tÞ is plotted as an example for four delays t and the
268101-2
week ending 27 DECEMBER 2013
PHYSICAL REVIEW LETTERS
PRL 111, 268101 (2013)
II(n=1,t)/IIdrift []
(a)
Ep = 1000 J 2.2
Ep = 500 J
2
Ep = 250 J Ep = 100 J
1.8 1.6
t=30 s
t=1.1 s
1.4 t=-200ns
t=200ns
1.2 1 0
1
2 3 45
10
20 30
100
50
200
delay t [ s]
(b) 2
10
S(n,qr,t) = a(t)·q r t 1
S(n=1,qr,t) [a.u.]
10
0
10
-1
10
-2
10
t = -200s t = 200ns t = 1.1 s t = 30 s
-3
10
-4
10
= 385.4nm = 359.3nm = 237.9nm = 335.2nm
= -2.3 = -2.3 = -2.6 = -2.3
-3
-2
10
10
q r [1/Å] wavelength
relative intensity [ ]
(c)
800
200
100
70
[nm] 50
40
35
3
t = 0.4 t = 1.1 t = 9.0 t = 13
2.5
s s s s
= 141.9nm = 127.5nm = 128.0nm = 141.0nm
2
1.5
1
0
0.005
0.01
0.015
0.02
-1
qr [Å ]
FIG. 2 (color). (a) Evolution of the integrated intensity IIðn ¼ 1; tÞ for the first diffuse Bragg sheet at laser energies of Ep ¼ 100 J (cross, dotted line), Ep ¼ 250 J (circle, dashed line), Ep ¼ 500 J (asterisk, solid line), and Ep ¼ 1000 J (square, dash-dotted line), curves corrected for drift and shifted for clarity. A steep increase on the 100 ns time scale is followed by a relaxation on the s time scale. Rise time and functional form of IIðn; tÞ vary with Ep . (b) The qz integrated structure factor Sðn ¼ 1; qr ; tÞ of the first order along with a power law fit Sðn; qr ; tÞ ¼ aðtÞqðtÞ for the four delays (t ¼ 200 ns, asterisk, black line; t ¼ 200 ns, circle, red line; t ¼ 1:1 s, cross, r blue line; t ¼ 30 s, triangle, green line) indicated in (a). A clear broadening of the Bragg sheet plateau and a steepened decay is most obvious for t ¼ 1:1 s. (c) Relative changes of the diffuse structure factor Sðn ¼ 1; qr ; tÞ=Sðn ¼ 1; qr ; 0Þ, as a function of undulation wavelength, for four selected time delays t, illustrating the spatial frequency and the time scale of the observed changes.
268101-3
PHYSICAL REVIEW LETTERS
PRL 111, 268101 (2013)
II(1,t) EMG r(1,t) (1,t) (1,t)
|X(n=1,t)| [] |Xdrift|
1.3 1.2
week ending 27 DECEMBER 2013
tr = 109ns, tf = 8.9 s < r(1,t)> = 277.9nm < (1,t)> = -2.39 < (1,t)> = 11.9nm
1.1
1 0.9 0.8 0
1
2
3 4 5
10
20
30 40 50
delay t [ s] FIG. 3 (color). Temporal evolution of the integrated intensity of the first order reflection IIð1; tÞ (diamond, black), lateral correlation length r ðtÞ (asterisk, blue line), line shape parameter ðtÞ (circle, red line), and smectic length scale ðtÞ (cross, green line) for laser excitation by pulses of 5 ns and Ep ¼ 200 J after normalization to the control (drift) measurements. The increase in diffuse intensity is followed by significant changes in the line shape parameters; e.g., the smectic length ðtÞ as well as r ðtÞ decrease to 85% within the first 2 s after excitation. Rise time tr ¼ 109 ns and decay constant tf ¼ 8:9 s of the intensity increase are determined from least squares fits of IIð1; tÞ to an exponentially modified Gaussian distribution (EMG) (magenta, solid line).
case of Ep ¼ 500 J corresponding to a peak intensity of Pp 5 104 W=cm2 . The t values have been chosen in view of the characteristic shape of the intensity trace in Fig. 2(a). Despite the experimental uncertainties in fitting of the exponent ðtÞ characterizing the lateral intensity decay, a clear steepening is observed, quantified by ððtÞ=drift Þ þ20% within t 1 s for the first order; see also Fig. 3. The steepening is accompanied by a decrease of the lateral correlation length ðr =drift Þ 40%. Conversely, the vertical correlations, quantified by the smectic length scale and the associated vertical correlation length z ¼ 1=q2r , transiently increase significantly beyond the equilibrium values during the relaxation pathway as evidenced from a sharpening of the Bragg sheet along qz ; see Fig. S2 in the Supplemental Material [15]. Finally, Fig. 2(c) illustrates the relative changes in the diffuse scattering factor Sð1; qr ; tÞ=Sð1; qr ; 0Þ, obtained after normalization of the curves shown in Fig. 2(b) to the unperturbed (equilibrium) line shape. This representation serves to identify the qr range at which the dynamics is centered, in other words, to quantify the spectrum of relevant undulation modes. A transient excitation of undulations in a well-defined wavelength band is observed on the 1 s time scale. The spectral distribution can be modeled by the line shape of an exponentially modified Gaussian (EMG). The model takes into account a Gaussian distribution of undulation wavelengths around a central undulation wavelength. The central wavelength ¼ 138 nm and bandwidth ¼ 63 nm as determined from nonlinear least squares fits are independent of t. Next, we turn to the temporal evolution of all drift normalized observables for the exemplary case of n ¼ 1,
shown in Fig. 3 for laser excitation by 5 ns and Ep ¼ 200 J pulses. The integrated intensity IIðn; tÞ exhibits a relatively fast rise time (tr 100 ns) and a relaxation behavior on a time scale of tf 10 s, which depends on the pulse parameters and n. For the integrated intensity of the first order IIðn ¼ 1; tÞ shown in Fig. 3, a rise time tr ¼ 109 ns and decay constant tf ¼ 8:9 s is determined from least squares fits of IIð1; tÞ to an exponentially modified Gaussian (EMG); see Supplemental Material for details [15]. All line shape effects, describing the functional form of the diffuse scattering, decay on the same 10 s time scale as the corresponding intensities IIðn; tÞ, but exhibit a rise time which is significantly longer, i.e., a factor of 5. By comparison of the temporal evolution for both laser pulse durations (see Fig. 3 and Fig. S1 in the Supplemental Material [15]) one can infer that temporal resolution is not limited by the pulse duration even for the longer pulse and that the integrated laser pulse energy Ep and not the peak intensity Pp triggers the observed dynamics. Furthermore, the amplitude in the relative changes was found to increase with the concentration of Texas red labeled lipids, and all effects vanished in control experiments without Texas red labeled lipids. These observations can well be interpreted in terms of a modulation instability as predicted and observed [20–22] for tensile forces perpendicular to the bilayer normal, acting on a mechanically quenched system. In the present case, the absorption processes associated with the laser pulse lead to molecular disorder and fluctuations (quantified by the observed increase in ) which favor a larger lateral area per lipid and hence a smaller bilayer thickness. Since the mechanical response of the lipid film with a macroscopic
268101-4
PRL 111, 268101 (2013)
PHYSICAL REVIEW LETTERS
thickness L and area is quenched on nanosecond time scales (similar to [23]), internal stress builds up which can be relaxed by buckling without large scale mass transport. Importantly, no variations of dðtÞ occur on these time scales in line with the experimental observation. According to [20–22], the free energy is minimized by the evolution of buckling pffiffiffiffiffiffiffiffiffiffiffi modes at a characteristic wavelength b ¼ 7 m and ¼ 6 nm (as, 2 L. For L 1300 54 A e.g., observed in Fig. S2 in the Supplemental Material [15]), one expects b 730 nm, which is on the same order of magnitude but still distinctly higher than the experimental result. This may be attributed to the fact that the time scale to build up buckling modes of optimum (larger) values is too long. In a multilamellar stack, the time scales to build up an undulation mode with a central wavelength of are expected to scale as ðÞ ¼ ð d=Þð=2Þ2 , in contrast to fluctuations of a free bilayer which are characterized by / 3 [24,25]. With a measured intermembrane sliding viscosity of 3 ¼ 0:016 Pa s for a similar lipid sample [26], a typical bilayer bending rigidity of ’ we obtain 14kB T, and a lamellar periodicity d ¼ 53:6 A, ’ 1 s for ¼ 138 nm, in excellent agreement with the observations in Fig. 3. In conclusion, the observed intensity changes are brought about by increased molecular disorder within the first 100 ns after excitation, followed by the formation of collective modes as a buckling (or modulation) instability peaking at 1 s. The characteristic wavelength of ¼ 138 63 nm is comparable to predictions for a buckling instability [20–22] in a multilamellar stack. Subsequent relaxation back to thermal equilibrium takes place on the 10 s time scale, possibly through a wide range of dissipation channels. Let us close with a short remark on the relevance of the present observations for widespread optical studies of biomolecular systems involving fluorescent markers. The laser intensities Pp 105 W=cm2 applied in the present experiment are significantly lower than those typically employed in confocal microscopy (Pp 106 W=cm2 ), two photon microscopy (Pp 1011 W=cm2 ), or superresolution by fluorescence switching (Pp 109 W=cm2 ). Despite the fact that pulse energies applied in microscopy experiments like STED are typically 1 order of magnitude smaller, the higher repetition rates of up to 100 MHz along with the higher peak intensities make it likely that similar collective dynamic effects occur in many photolabeled soft matter sample systems, effectively driving the structure away from thermal equilibrium. The associated effects may not directly manifest themselves on molecular length scales, but rather on mesoscopic scales via collective mechanisms. We thank Christina Bo¨mer and Christian Holme for help during the beam time, and Dr. Jo¨rg Hallmann for a related collaboration in a preceding experiment as
week ending 27 DECEMBER 2013
well as Marcus Mu¨ller for helpful discussions. Financial support by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) through SFB 937 is gratefully acknowledged.
*[email protected] [1] J. Prost and R. Bruinsma, Europhys. Lett. 33, 321 (1996). [2] J. Prost, J. B. Manneville, and R. Bruinsma, Eur. Phys. J. B 1, 465 (1998). [3] S. Sankararaman, G. I. Menon, and P. B. Sunil Kumar, Phys. Rev. E 66, 031914 (2002). [4] S. Ramaswamy, J. Toner, and J. Prost, Pramana 53, 237 (1999); Phys. Rev. Lett. 84, 3494 (2000). [5] H. Y. Chen, Phys. Rev. Lett. 92, 168101 (2004). [6] N. Gov, Phys. Rev. Lett. 93, 268104 (2004). [7] L. C. L. Lin, N. Gov, and F. L. H. Brown, J. Chem. Phys. 124, 074903 (2006). [8] J. B. Manneville, P. Bassereau, D. Le´vy, and J. Prost, Phys. Rev. Lett. 82, 4356 (1999). [9] J. B. Manneville, P. Bassereau, S. Ramaswamy, and J. Prost, Phys. Rev. E 64, 021908 (2001). [10] P. Girard, J. Prost, and P. Bassereau, Phys. Rev. Lett. 94, 088102 (2005). [11] J. A. Titus, R. Haugland, S. O. Sharrow, and D. M. Segal, J. Immunol. Methods 50, 193 (1982). [12] M. J. Skaug, M. L. Longo, and R. Faller, J. Phys. Chem. B 115, 8500 (2011). [13] W. Helfrich, Z. Naturforsch. C 28, 693 (1973). [14] T. Salditt, M. Vogel, and W. Fenzl, Phys. Rev. Lett. 90, 178101 (2003). [15] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.111.268101 for details on the experiment, the line shape analysis, and additional plots on the temporal evolution of membrane structural parameters. [16] D. Constantin, C. Ollinger, M. Vogel, and T. Salditt, Eur. Phys. J. E 18, 273 (2005). [17] U. Mennicke, D. Constantin, and T. Salditt, Eur. Phys. J. E 20, 221 (2006). [18] M. Wulff, A. Plech, L. Eybert, R. Randler, F. Schotte, and P. Anfinrud, Faraday Discuss. 122, 13 (2003). [19] T. Reusch, Non-Equilibrium Dynamics of Lipid Bilayers (Ph.D. Thesis), Go¨ttingen Series in X-ray Physics (Universita¨tsverlag Go¨ttingen, Go¨ttingen, 2013) Vol. 12. [20] M. Delaye, R. Ribotta, and G. Durand, Phys. Lett. 44A, 139 (1973). [21] J. Prost and P. G. deGennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, England, 1993), 2nd ed. [22] Z. G. Wang, J. Chem. Phys. 100, 2298 (1994). [23] M. Cammarata et al., J. Chem. Phys. 124, 124504 (2006). [24] A. G. Zilman and R. Granek, Phys. Rev. Lett. 77, 4788 (1996). [25] T. Takeda, Y. Kawabata, H. Seto, S. Komura, S. K. Ghosh, M. Nagao, and D. Okuhara, J. Phys. Chem. Solids 60, 1375 (1999). [26] M. C. Rheinsta¨dter, W. Ha¨ußler, and T. Salditt, Phys. Rev. Lett. 97, 048103 (2006).
268101-5
PHYSICAL REVIEW LETTERS
week ending 27 DECEMBER 2013
Nonequilibrium Collective Dynamics in Photoexcited Lipid Multilayers by Time Resolved Diffuse X-Ray Scattering T. Reusch,1,* D. D. Mai,1 M. Osterhoff,1 D. Khakhulin,2 M. Wulff,2 and T. Salditt1,* 1
Institut fu¨r Ro¨ntgenphysik, Georg-August-Universita¨t Go¨ttingen, Friedrich-Hund-Platz 1, 37077 Go¨ttingen, Germany 2 European Synchrotron Radiation Facility (ESRF), 6 rue Jules Horowitz, 38000 Grenoble, France (Received 7 June 2013; published 26 December 2013) We study the nonequilibrium shape fluctuations in fluorescence labeled phospholipid multibilayers composed of the model lipid DOPC and the well-known lipid dye Texas red, driven out of equilibrium by short laser pulses. The temporal evolution of the lipid bilayer undulations after excitation was recorded by time resolved x-ray diffraction. Already at moderate peak intensities (Pp 105 W=cm2 ), pulsed laser illumination leads to significant changes of the undulation modes in a well-defined lateral wavelength band. The observed phenomena evolve on nano- to microsecond time scales after optical excitation, and can be described in terms of a modulation instability in the lipid multilamellar stack. DOI: 10.1103/PhysRevLett.111.268101
PACS numbers: 87.16.dj, 05.70.Ln, 87.64.Bx, 87.64.kv
Excitation of embedded fluorophores in biomolecular assemblies is a ubiquitous tool in modern biophysics. Despite the excitations from the molecular ground state of the fluorophores, it is tacitly assumed in most experiments that the supramolecular collective states of the entire biomolecular assembly remain unchanged, apart perhaps from more or less negligible heat generation. At the same time, it is well understood that collective modes in soft matter systems can easily be excited, and that even small local forces or energy can lead to a rather large structural response. More generally, all active and all living systems are intrinsically out of thermal equilibrium, in many cases driven by a multitude of local force centers and by energy release on molecular scales, for example, due to metabolism. From a fundamental point of view, the understanding of the dissipation pathway from local energy input to heat, eventually accompanied by various collective modes, remains mysterious in many cases. For the important case of membranes, considered to be nature’s most important interface, nonequilibrium fluctuations driven by active force centers, such as proteins, have been addressed in a number of theoretical studies [1–7]. On the contrary, on the experimental side only few studies, for example, by micropipette aspiration and optical microscopy, have tried to address this challenging issue [8–10]. In this work we show that photoexcitation of individual fluorophores in a labeled lipid membrane can lead to a collective response and address the question over which pathway and on which time scales structural dynamics evolve. We have investigated fluorescently labeled phospholipid multibilayers composed of the model lipid
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
0031-9007=13=111(26)=268101(5)
1,2-Dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) and the well-known lipid dye Texas red [11,12] by time resolved x-ray scattering after excitation by a nanosecond laser pulse, covering a broad range of well-matched length and time scales from near-molecular to the mesoscopic range. The evolution of the membrane height-height correlation functions was monitored by recording the diffuse (nonspecular) x-ray reflectivity in a stroboscopic manner synchronized to the periodic optical excitation. In this laser-pump x-ray-probe scheme, pronounced deviations of the collective undulation spectra from thermal equilibrium are observed, which is usually described within linearized smectic elasticity, based on two elastic coefficients, the compressional modulus B and the bending modulus K ¼ =d, where is the single bilayer bending rigidity and d the lamellar periodicity [13]. Figure 1(a) shows a schematic of the ‘‘optical pump–x-ray-probe’’ principle used to characterize the structural and dynamical response of the fluorophore labeled lipid membranes to pulsed laser illumination. (1) Membrane dynamics are excited (or pumped) by a short nanosecond laser pulse. (2) At a well-defined time delay t after the excitation, the instantaneous sample structure is probed by a short ( 50 ps) x-ray pulse. (3) The pump-probe scheme is repeated in a stroboscopic manner for each time delay t until a suitable signal-to-noise ratio is reached. Changing t now allows us to observe characteristic changes in the membrane height-height correlation functions following a short pulse excitation, in particular, by extracting the fundamental length scales describing the collective membrane undulations as a function of t: (i) the lamellar periodicity d, (ii) the rms-fluctuation amplitude ¼ hui ðrÞ2 ir;i (i denotes the index of bilayer in the multilamellar stack), (iii) the in-plane correlation length r , and (iv) the vertical correlation length z ðqr Þ ¼ 1=ðq2r Þ, which describes the correlation length in the direction z normal to the membranes, for an undulation with lateral
268101-1
Published by the American Physical Society
0
10
(b)
t
probe-pulse 0.20 pump-pulse nm 1.)
(g)
-4
10
-5
1st. order
1st. order S(n,qr) ~ qr qr* = 1.7·10 -3Å -1, = -2.4 -3
10
-2
II(1,t)
kf 0.05
10
12
(c)
1.10
1.05
PB
3.) 0
0.04 0.08 qr [1/Å]
-0.01
undulation modes
-1
qr [Å-1]10
x 10 1.20 FWHM qz 1.15
0 qr [1/Å]
0.01
d
(f)
-1
0.10 2.)
-3
lateral correlation length r
transverse correlation length z
-2
10
qz [1/Å]
1.) excitation 2.) measurement 3.) relaxation
(d)
10
10
qz [1/Å]
ki
SB 0.15
HWHM (qr*)
-1
10
FWHMqz [1/Å]
0.25
ki
S(n,qr) [a.u.]
(a)
week ending 27 DECEMBER 2013
PHYSICAL REVIEW LETTERS
PRL 111, 268101 (2013)
x 10
10
-3
FWHM of 1st. reflection
2 qr2 +
res
8 6
(e)
4 2 0
1
2
3 4 qr [1/Å]
5
x 10-3 7 6
FIG. 1 (color). (a) Schematic of a laser pump–x-ray-probe measurement on a multilamellar lipid stack in the fluid L phase. The temporal evolution of membrane undulations is studied in response to a short pulse excitation, by recording the diffuse scattering pattern and line shape analysis of the individual lamellar reflections. (b) Example of a lamellar diffraction pattern with primary beam (PB), specular beam (SB), and the two first lamellar diffraction orders, with (c) a close-up of the first order reflection n ¼ 1. From the two-dimensional distribution, the lateral decay with qr as shown in (d) and the width in direction of qz as shown in (e) are extracted, to yield the temporal evolution of (f) lateral r and vertical z correlation lengths, respectively. (g) Sample chamber for oriented Texas red labeled lipid multilayers fully immersed in solution.
wave number qr . In thermal equilibrium the prefactor is pffiffiffiffiffiffiffiffiffiffi given by the so-called smectic penetration length K=B. These length scales and correlation functions are derived from the measured structure factor Sðqz ; qr Þ, which describes the diffuse intensity distribution around the equidistant lamellar diffraction orders at qz ¼ nð2=dÞ. To this end the Sðqr ; qz Þ measured for each time delay is analyzed as follows. First, intensity is integrated in the range qz ðnÞ ð=dÞ for each diffraction order n, resulting in a structure factor Sðn; qr Þ of an average single bilayer [14]. Sðn; qr Þ exhibits a rather flat plateau for qr qr ¼ 2=r and then falls off with a characteristic power law decay Sðn;qr Þ / aq r at large qr [14]; see Fig. 1(d). For qz 1, in particular, for n ¼ 1, the width qr of the plateau is a measure of the in-plane correlation length r ¼ ð2=HWHMÞ and Sðqr ; qz Þ is identified with the Fourier transform of the in-plane self-correlation function of an average bilayer. In a second step, is extracted from the increase of the Bragg sheet width along qz as a function of qr , see Fig. 1(e), characterizing the height-height crosscorrelation between different bilayers, as detailed in the Supplemental Material [15]. The experimental data shown here were recorded on highly oriented DOPC multilayers (N 1300 bilayers) containing 5 mole % Texas red labeled DHPE (headgroup labeled). Samples were fully immersed in a solution containing 30 wt % polyethylene glycol (corresponding to an osmotic stress of 1.54 MPa), preventing destabilization of the multilayers [16,17]. The 17 keV x-ray undulator beam impinged onto the sample at angle of incidence i 0:5 . Stroboscopic data accumulation was carried out at a repetition rate of f 1 kHz [18] with synchronized optical pumping using ¼ 527 nm, well matched to the edge of the absorption spectrum of Texas red [11]. The standard
laser pulse duration was 180 ns, while some data were recorded at increased temporal resolution of 5 ns, roughly corresponding to the lifetime of the excited state. Full details are given in the Supplemental Material [15,19]. Figure 2 shows the temporal evolution of the diffuse scattering intensity pattern highlighting the main changes in the line shape, followed by Fig. 3 which presents the relative changes in all observables extracted from the first diffraction order. The first generic observable is the time dependent integrated intensity IIðn; tÞ of the individual reflection orders n, as plotted in Fig. 2(a) for n ¼ 1 and four different pump energies Ep . A sharp intensity increase within the first 1 s after optical excitation is observed in all cases, the functional form of IIðn; tÞ as well as the relative amplitude both depend on the pump energy Ep as well as n. The rise time of the initial intensity increase shortens with pump energy, from t 1 s for Ep 100 J to t 100 ns for Ep 1000 J. Relaxation to thermal equilibrium takes place on the 10 s time scale, and the system has fully relaxed after t ¼ 100 s in all cases. A distinct second intensity maximum at t 40 s is observed for the second diffuse order; see Fig. S1 in the Supplemental Material [15]. The fast intensity increase can be linked to an increased positional disorder of the membranes upon laser excitation. The intensity relaxation on the s time scale (a broad plateau for Ep 500 J) can be attributed to the energy dissipation via collective modes, possibly a collective undulation amplitude. The bilayer as determined periodicity dðtÞ ¼ ðn2=qz ðnÞÞ ¼ 53:6 A from peak positions (center of mass) remains unchanged in all cases. Next, line shape changes were investigated in addition to the intensity; see Figs. 2(b) and 2(c). The lateral momentum dependence of the integrated structure factor Sðn; qr ; tÞ is plotted as an example for four delays t and the
268101-2
week ending 27 DECEMBER 2013
PHYSICAL REVIEW LETTERS
PRL 111, 268101 (2013)
II(n=1,t)/IIdrift []
(a)
Ep = 1000 J 2.2
Ep = 500 J
2
Ep = 250 J Ep = 100 J
1.8 1.6
t=30 s
t=1.1 s
1.4 t=-200ns
t=200ns
1.2 1 0
1
2 3 45
10
20 30
100
50
200
delay t [ s]
(b) 2
10
S(n,qr,t) = a(t)·q r t 1
S(n=1,qr,t) [a.u.]
10
0
10
-1
10
-2
10
t = -200s t = 200ns t = 1.1 s t = 30 s
-3
10
-4
10
= 385.4nm = 359.3nm = 237.9nm = 335.2nm
= -2.3 = -2.3 = -2.6 = -2.3
-3
-2
10
10
q r [1/Å] wavelength
relative intensity [ ]
(c)
800
200
100
70
[nm] 50
40
35
3
t = 0.4 t = 1.1 t = 9.0 t = 13
2.5
s s s s
= 141.9nm = 127.5nm = 128.0nm = 141.0nm
2
1.5
1
0
0.005
0.01
0.015
0.02
-1
qr [Å ]
FIG. 2 (color). (a) Evolution of the integrated intensity IIðn ¼ 1; tÞ for the first diffuse Bragg sheet at laser energies of Ep ¼ 100 J (cross, dotted line), Ep ¼ 250 J (circle, dashed line), Ep ¼ 500 J (asterisk, solid line), and Ep ¼ 1000 J (square, dash-dotted line), curves corrected for drift and shifted for clarity. A steep increase on the 100 ns time scale is followed by a relaxation on the s time scale. Rise time and functional form of IIðn; tÞ vary with Ep . (b) The qz integrated structure factor Sðn ¼ 1; qr ; tÞ of the first order along with a power law fit Sðn; qr ; tÞ ¼ aðtÞqðtÞ for the four delays (t ¼ 200 ns, asterisk, black line; t ¼ 200 ns, circle, red line; t ¼ 1:1 s, cross, r blue line; t ¼ 30 s, triangle, green line) indicated in (a). A clear broadening of the Bragg sheet plateau and a steepened decay is most obvious for t ¼ 1:1 s. (c) Relative changes of the diffuse structure factor Sðn ¼ 1; qr ; tÞ=Sðn ¼ 1; qr ; 0Þ, as a function of undulation wavelength, for four selected time delays t, illustrating the spatial frequency and the time scale of the observed changes.
268101-3
PHYSICAL REVIEW LETTERS
PRL 111, 268101 (2013)
II(1,t) EMG r(1,t) (1,t) (1,t)
|X(n=1,t)| [] |Xdrift|
1.3 1.2
week ending 27 DECEMBER 2013
tr = 109ns, tf = 8.9 s < r(1,t)> = 277.9nm < (1,t)> = -2.39 < (1,t)> = 11.9nm
1.1
1 0.9 0.8 0
1
2
3 4 5
10
20
30 40 50
delay t [ s] FIG. 3 (color). Temporal evolution of the integrated intensity of the first order reflection IIð1; tÞ (diamond, black), lateral correlation length r ðtÞ (asterisk, blue line), line shape parameter ðtÞ (circle, red line), and smectic length scale ðtÞ (cross, green line) for laser excitation by pulses of 5 ns and Ep ¼ 200 J after normalization to the control (drift) measurements. The increase in diffuse intensity is followed by significant changes in the line shape parameters; e.g., the smectic length ðtÞ as well as r ðtÞ decrease to 85% within the first 2 s after excitation. Rise time tr ¼ 109 ns and decay constant tf ¼ 8:9 s of the intensity increase are determined from least squares fits of IIð1; tÞ to an exponentially modified Gaussian distribution (EMG) (magenta, solid line).
case of Ep ¼ 500 J corresponding to a peak intensity of Pp 5 104 W=cm2 . The t values have been chosen in view of the characteristic shape of the intensity trace in Fig. 2(a). Despite the experimental uncertainties in fitting of the exponent ðtÞ characterizing the lateral intensity decay, a clear steepening is observed, quantified by ððtÞ=drift Þ þ20% within t 1 s for the first order; see also Fig. 3. The steepening is accompanied by a decrease of the lateral correlation length ðr =drift Þ 40%. Conversely, the vertical correlations, quantified by the smectic length scale and the associated vertical correlation length z ¼ 1=q2r , transiently increase significantly beyond the equilibrium values during the relaxation pathway as evidenced from a sharpening of the Bragg sheet along qz ; see Fig. S2 in the Supplemental Material [15]. Finally, Fig. 2(c) illustrates the relative changes in the diffuse scattering factor Sð1; qr ; tÞ=Sð1; qr ; 0Þ, obtained after normalization of the curves shown in Fig. 2(b) to the unperturbed (equilibrium) line shape. This representation serves to identify the qr range at which the dynamics is centered, in other words, to quantify the spectrum of relevant undulation modes. A transient excitation of undulations in a well-defined wavelength band is observed on the 1 s time scale. The spectral distribution can be modeled by the line shape of an exponentially modified Gaussian (EMG). The model takes into account a Gaussian distribution of undulation wavelengths around a central undulation wavelength. The central wavelength ¼ 138 nm and bandwidth ¼ 63 nm as determined from nonlinear least squares fits are independent of t. Next, we turn to the temporal evolution of all drift normalized observables for the exemplary case of n ¼ 1,
shown in Fig. 3 for laser excitation by 5 ns and Ep ¼ 200 J pulses. The integrated intensity IIðn; tÞ exhibits a relatively fast rise time (tr 100 ns) and a relaxation behavior on a time scale of tf 10 s, which depends on the pulse parameters and n. For the integrated intensity of the first order IIðn ¼ 1; tÞ shown in Fig. 3, a rise time tr ¼ 109 ns and decay constant tf ¼ 8:9 s is determined from least squares fits of IIð1; tÞ to an exponentially modified Gaussian (EMG); see Supplemental Material for details [15]. All line shape effects, describing the functional form of the diffuse scattering, decay on the same 10 s time scale as the corresponding intensities IIðn; tÞ, but exhibit a rise time which is significantly longer, i.e., a factor of 5. By comparison of the temporal evolution for both laser pulse durations (see Fig. 3 and Fig. S1 in the Supplemental Material [15]) one can infer that temporal resolution is not limited by the pulse duration even for the longer pulse and that the integrated laser pulse energy Ep and not the peak intensity Pp triggers the observed dynamics. Furthermore, the amplitude in the relative changes was found to increase with the concentration of Texas red labeled lipids, and all effects vanished in control experiments without Texas red labeled lipids. These observations can well be interpreted in terms of a modulation instability as predicted and observed [20–22] for tensile forces perpendicular to the bilayer normal, acting on a mechanically quenched system. In the present case, the absorption processes associated with the laser pulse lead to molecular disorder and fluctuations (quantified by the observed increase in ) which favor a larger lateral area per lipid and hence a smaller bilayer thickness. Since the mechanical response of the lipid film with a macroscopic
268101-4
PRL 111, 268101 (2013)
PHYSICAL REVIEW LETTERS
thickness L and area is quenched on nanosecond time scales (similar to [23]), internal stress builds up which can be relaxed by buckling without large scale mass transport. Importantly, no variations of dðtÞ occur on these time scales in line with the experimental observation. According to [20–22], the free energy is minimized by the evolution of buckling pffiffiffiffiffiffiffiffiffiffiffi modes at a characteristic wavelength b ¼ 7 m and ¼ 6 nm (as, 2 L. For L 1300 54 A e.g., observed in Fig. S2 in the Supplemental Material [15]), one expects b 730 nm, which is on the same order of magnitude but still distinctly higher than the experimental result. This may be attributed to the fact that the time scale to build up buckling modes of optimum (larger) values is too long. In a multilamellar stack, the time scales to build up an undulation mode with a central wavelength of are expected to scale as ðÞ ¼ ð d=Þð=2Þ2 , in contrast to fluctuations of a free bilayer which are characterized by / 3 [24,25]. With a measured intermembrane sliding viscosity of 3 ¼ 0:016 Pa s for a similar lipid sample [26], a typical bilayer bending rigidity of ’ we obtain 14kB T, and a lamellar periodicity d ¼ 53:6 A, ’ 1 s for ¼ 138 nm, in excellent agreement with the observations in Fig. 3. In conclusion, the observed intensity changes are brought about by increased molecular disorder within the first 100 ns after excitation, followed by the formation of collective modes as a buckling (or modulation) instability peaking at 1 s. The characteristic wavelength of ¼ 138 63 nm is comparable to predictions for a buckling instability [20–22] in a multilamellar stack. Subsequent relaxation back to thermal equilibrium takes place on the 10 s time scale, possibly through a wide range of dissipation channels. Let us close with a short remark on the relevance of the present observations for widespread optical studies of biomolecular systems involving fluorescent markers. The laser intensities Pp 105 W=cm2 applied in the present experiment are significantly lower than those typically employed in confocal microscopy (Pp 106 W=cm2 ), two photon microscopy (Pp 1011 W=cm2 ), or superresolution by fluorescence switching (Pp 109 W=cm2 ). Despite the fact that pulse energies applied in microscopy experiments like STED are typically 1 order of magnitude smaller, the higher repetition rates of up to 100 MHz along with the higher peak intensities make it likely that similar collective dynamic effects occur in many photolabeled soft matter sample systems, effectively driving the structure away from thermal equilibrium. The associated effects may not directly manifest themselves on molecular length scales, but rather on mesoscopic scales via collective mechanisms. We thank Christina Bo¨mer and Christian Holme for help during the beam time, and Dr. Jo¨rg Hallmann for a related collaboration in a preceding experiment as
week ending 27 DECEMBER 2013
well as Marcus Mu¨ller for helpful discussions. Financial support by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) through SFB 937 is gratefully acknowledged.
*[email protected] [1] J. Prost and R. Bruinsma, Europhys. Lett. 33, 321 (1996). [2] J. Prost, J. B. Manneville, and R. Bruinsma, Eur. Phys. J. B 1, 465 (1998). [3] S. Sankararaman, G. I. Menon, and P. B. Sunil Kumar, Phys. Rev. E 66, 031914 (2002). [4] S. Ramaswamy, J. Toner, and J. Prost, Pramana 53, 237 (1999); Phys. Rev. Lett. 84, 3494 (2000). [5] H. Y. Chen, Phys. Rev. Lett. 92, 168101 (2004). [6] N. Gov, Phys. Rev. Lett. 93, 268104 (2004). [7] L. C. L. Lin, N. Gov, and F. L. H. Brown, J. Chem. Phys. 124, 074903 (2006). [8] J. B. Manneville, P. Bassereau, D. Le´vy, and J. Prost, Phys. Rev. Lett. 82, 4356 (1999). [9] J. B. Manneville, P. Bassereau, S. Ramaswamy, and J. Prost, Phys. Rev. E 64, 021908 (2001). [10] P. Girard, J. Prost, and P. Bassereau, Phys. Rev. Lett. 94, 088102 (2005). [11] J. A. Titus, R. Haugland, S. O. Sharrow, and D. M. Segal, J. Immunol. Methods 50, 193 (1982). [12] M. J. Skaug, M. L. Longo, and R. Faller, J. Phys. Chem. B 115, 8500 (2011). [13] W. Helfrich, Z. Naturforsch. C 28, 693 (1973). [14] T. Salditt, M. Vogel, and W. Fenzl, Phys. Rev. Lett. 90, 178101 (2003). [15] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.111.268101 for details on the experiment, the line shape analysis, and additional plots on the temporal evolution of membrane structural parameters. [16] D. Constantin, C. Ollinger, M. Vogel, and T. Salditt, Eur. Phys. J. E 18, 273 (2005). [17] U. Mennicke, D. Constantin, and T. Salditt, Eur. Phys. J. E 20, 221 (2006). [18] M. Wulff, A. Plech, L. Eybert, R. Randler, F. Schotte, and P. Anfinrud, Faraday Discuss. 122, 13 (2003). [19] T. Reusch, Non-Equilibrium Dynamics of Lipid Bilayers (Ph.D. Thesis), Go¨ttingen Series in X-ray Physics (Universita¨tsverlag Go¨ttingen, Go¨ttingen, 2013) Vol. 12. [20] M. Delaye, R. Ribotta, and G. Durand, Phys. Lett. 44A, 139 (1973). [21] J. Prost and P. G. deGennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, England, 1993), 2nd ed. [22] Z. G. Wang, J. Chem. Phys. 100, 2298 (1994). [23] M. Cammarata et al., J. Chem. Phys. 124, 124504 (2006). [24] A. G. Zilman and R. Granek, Phys. Rev. Lett. 77, 4788 (1996). [25] T. Takeda, Y. Kawabata, H. Seto, S. Komura, S. K. Ghosh, M. Nagao, and D. Okuhara, J. Phys. Chem. Solids 60, 1375 (1999). [26] M. C. Rheinsta¨dter, W. Ha¨ußler, and T. Salditt, Phys. Rev. Lett. 97, 048103 (2006).
268101-5
